Question

Convert (126)10 to binary.

Answer 1

`126_(10)=1111110_2`

Step-by-step explanation:

In order to get this convertion done, we have to divide by two the decimal number, take note of the quotient and reminder, then divide the result by two until the result of the division is zero.

`126| 2`

`quotient_1=63\\remainder_1=0`

`63| 2`

`quotient_2=31\\remainder_2=1`

`31| 2`

`quotient_3=15\\remainder_3=1`

`15| 2`

`quotient_4=7\\remainder_4=1`

`7| 2`

`quotient_5=3\\remainder_5=1`

`3| 2`

`quotient_6=1\\remainder_6=1`

`1| 2`

`quotient_7=0\\remainder_7=1`

Now the last remainder is the most significant bit, and the first remainder the least significative, so:

`126_(10)=1111110_2`